Details

analyze266.0ms (3.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	248×	body	128	valid
9.0ms	276×	pre	128	true
1.0ms	20×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 26.8b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series532.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4883	1979
1	4883	1979

prune173.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.4b

Counts

87 → 5

Compiler

Compiled 3458 to 2256 computations (34.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 99

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series893.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
316.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4963	3037
1	4963	3037

prune679.0ms (9.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	3	0	3
Picked	1	0	1
Done	1	0	1
Total	107	9	116

Merged error: 0.0b

Counts

116 → 9

Compiler

Compiled 14416 to 10028 computations (30.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series670.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
134.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5109	1969

prune316.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 0b

Counts

93 → 9

Compiler

Compiled 6818 to 4698 computations (31.1% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))))
0.3b	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
0.4b	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.8b	(pow.f64 (*.f64 a c) 3)

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`*-un-lft-identity_binary64`
16×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow-prod-down_binary64` `associate-/r*_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `associate-/l_binary64` `div-exp_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 107

Calls

4 calls:

26.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))))
14.0ms	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
12.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
4.0ms	(pow.f64 (*.f64 a c) 3)

series1.1s (15.5%)

Counts

4 → 12

Calls

4 calls:

566.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))))
297.0ms	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
137.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
74.0ms	(pow.f64 (*.f64 a c) 3)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4958	4770
1	4958	4770

prune315.0ms (4.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 0b

Counts

128 → 9

Compiler

Compiled 6508 to 4188 computations (35.6% saved)

regimes80.0ms (1.2%)

Compiler: Compiled 933 to 684 computations (26.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample1.2s (17.6%)

Algorithm

1×

intervals

Results

392.0ms	7665×	body	128	valid
271.0ms	8812×	pre	128	true
42.0ms	812×	body	128	nan
35.0ms	335×	body	256	valid

Compiler

Compiled 355 to 262 computations (26.2% saved)

Details

analyze266.0ms (3.8%)

sample32.0ms (0.5%)

simplify73.0ms (1.1%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite39.0ms (0.6%)

series532.0ms (7.7%)

simplify85.0ms (1.2%)

prune173.0ms (2.5%)

localize15.0ms (0.2%)

rewrite56.0ms (0.8%)

series893.0ms (12.9%)

simplify77.0ms (1.1%)

prune679.0ms (9.8%)

localize12.0ms (0.2%)

rewrite32.0ms (0.5%)

series670.0ms (9.7%)

simplify70.0ms (1%)

prune316.0ms (4.6%)

localize29.0ms (0.4%)

rewrite76.0ms (1.1%)

series1.1s (15.5%)

simplify93.0ms (1.3%)

prune315.0ms (4.6%)

regimes80.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (17.6%)

Profiling